There's a number of reasons for that, tl;dr reason below;
Because Gardevoir is Lily's favorite Pokemon and the only one she can bring herself to care about now that's she fallen out of interest with the franchise. If you want even more evidence of this outside of the comic (and have absolutely nothing better to do with your time) check out her wiki on the Mad House and look at how much she's written about the other 1000 Pokemon and see how much it absolutely pales in comparison to the things she's written about Gardevoir's alone. Seriously, I'm not exaggerating when I say I've seen other Tumblr art blogs who revolve around a single Pokemon include or involve other Pokemon far more then Poke-mad House. I don't think I'm exaggerating when I say that Lily should change the name to "Gardevoir Mad House" at this point as the comic has so little to do with the Pokemon Universe outside of Gardevoir.
It fairly obvious that Lily has a thing for Gardevoirs (or at least thier design) and generally likes their powers and what they're capable off, but doesn't like the actual lore behind the Pokemon, so the comic is her way of bringing what she wants Gardevoir to be to life. It's also clear, from looking at the interests she has throughout her time on the internet (WoW, MLP, Star Wars, SU, ect.) that she tends to enjoy fantasy settings and stories, be they medieval, sci-fi, urban, or otherwise. Pokemon does has some fantastical elements, but I wouldn't quite call it a straight-up fantasy, it's more of a mis-mash of several types of genre's making it sort of its own thing which doesn't really "do it" enough for Lily. If I could make a guess, Lily seems to be trying to turn "Gardevoir" into a fantasy-style creature that wouldn't be too out of place as a race in World of Warcraft or Star Wars or the like.
She also seems to like Romance orientated stories with a bit of Action thrown in, as shown in pretty much all of her fan fics and general interests. She particularly seems to like the idea of having a strong, bad-ass women as her partner with a bit of a soft side that they only show to her, or a character that she can project onto (as you can see with the Gardevoirs, Sylvanas, Rey), and even depend on her to some level, sometimes to an unnerving degree. They're are different flavor's of this, sure, but all the character's Lily has "waifu-ized" generally share these traits, and that's what make her concept of Gardevoir's so appealing to her and why pretty much every significant Gardevoir is in a relationship, usually with a human.
Anyways Son Goku Baku, let's finally get to the point of your question:
Lily's basically taken apart what a Gardevoir is in the lore and changed or flat out gotten rid of so many important aspects of The Pokemon Universe in her comic and remade Gardevoirs to basically be a "super powered waifu-slave race" that could be fit into any fantasy setting. Gardevoirs design and abilities are appealing yet still simple enough that she can alter, tweek, and/or add to it to suit her tastes of the week, making it easy for her to focus on or come up with new "members" of Gardevoir that suit her liking and ship them with whoever she likes. Though often time Gardevoirs just seem like a place holder or a "different" flavor to various other major characters Lily's into while Lily's looking for a character to fill that niche' or is just looking for a "break" from the main thing (ie: G, the main Gardevoir, is clearly a Sylvanas fill in, I haven't read her Star Wars fic, Marah could be a chubby stand if for "innocent" Rey while the sickly Gardevoir could be "dark jedi" Rey, and I'm sure there's a few others that people could draw comparisons to, I'm not even going to get into what repressed desires Bonnie represents). We haven't seen many more because Lily's probably content with Sylvanas and Rey right now, but give it another year or two and we might see Lily pick up the comic a bit again, unless she finds another franchise that has a girl that suits her taste. Most likely a franchise that many consider have "jumped the shark" so Lily can shove her self-insert into it under the guise of "fixing it".
tl;dr: Lily likes Gardevoirs and always pairs them with people because, through her comic, she's created a world where Gardevoirs serve as her "flavor of the month" fetish-waifu's.
